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The barrel of a fountain-pen, cylindrical in shape is $7 cm$ long and $5 mm$ in diameter. A full barrel of ink in the pen is used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre?

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742524

86555

48000

54000

answer is C.

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Detailed Solution

Given a barrel of a fountain-pen, cylindrical in shape is 7 cm long and 5 mm in diameter.
A full barrel of ink in the pen is used up on writing 330 words on an average.
The diameter of the cylindrical barrel is

5 mm = 510 cm .

Therefore, its radius

0.5 2 cm = 0. 25 cm .

The volume of the cylinder is

V = π r 2 h

, here r is radius, h is height.
Then the volume of the cylindrical barrel is,

V = 227 × 0.25 2 × 7 ⇒ V = 9.6250 7 ⇒ V = 1.3750 cm 3

The volume of ink in the bottle,

15 of a litre = 15 × 1000 ⇒ 200 cm 3

The total number of barrels required to fill from the volume of ink is

200 1.375

.
So, the number of words required is,

200 1.375 × 330 = 48000

Thus, the number of words required is 48,000.
Therefore, option (3) is correct.

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